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target/
**/*.rs.bk
Cargo.lock

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[package]
name = "ff"
version = "0.4.0"
authors = ["Sean Bowe <ewillbefull@gmail.com>"]
description = "Library for building and interfacing with finite fields"
documentation = "https://docs.rs/ff/"
homepage = "https://github.com/ebfull/ff"
license = "MIT/Apache-2.0"
repository = "https://github.com/ebfull/ff"
[dependencies]
byteorder = "1"
rand = "0.4"
ff_derive = { version = "0.3.0", path = "ff_derive", optional = true }
[features]
default = []
derive = ["ff_derive"]

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The MIT License (MIT)
Copyright (c) 2017 Sean Bowe
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
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THE SOFTWARE.

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# ff
`ff` is a finite field library written in pure Rust, with no `unsafe{}` code.
## Disclaimers
* This library does not provide constant-time guarantees.
## Usage
Add the `ff` crate to your `Cargo.toml`:
```toml
[dependencies]
ff = "0.4"
```
The `ff` crate contains `Field`, `PrimeField`, `PrimeFieldRepr` and `SqrtField` traits. See the **[documentation](https://docs.rs/ff/0.4.0/ff/)** for more.
### #![derive(PrimeField)]
If you need an implementation of a prime field, this library also provides a procedural macro that will expand into an efficient implementation of a prime field when supplied with the modulus. `PrimeFieldGenerator` must be an element of Fp of p-1 order, that is also quadratic nonresidue.
First, enable the `derive` crate feature:
```toml
[dependencies]
ff = { version = "0.4", features = ["derive"] }
```
And then use the macro like so:
```rust
extern crate rand;
#[macro_use]
extern crate ff;
#[derive(PrimeField)]
#[PrimeFieldModulus = "52435875175126190479447740508185965837690552500527637822603658699938581184513"]
#[PrimeFieldGenerator = "7"]
struct Fp(FpRepr);
```
And that's it! `Fp` now implements `Field` and `PrimeField`. `Fp` will also implement `SqrtField` if supported. The library implements `FpRepr` itself and derives `PrimeFieldRepr` for it.
## License
Licensed under either of
* Apache License, Version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
* MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
at your option.
### Contribution
Unless you explicitly state otherwise, any contribution intentionally
submitted for inclusion in the work by you, as defined in the Apache-2.0
license, shall be dual licensed as above, without any additional terms or
conditions.

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[package]
name = "ff_derive"
version = "0.3.0"
authors = ["Sean Bowe <ewillbefull@gmail.com>"]
description = "Procedural macro library used to build custom prime field implementations"
documentation = "https://docs.rs/ff/"
homepage = "https://github.com/ebfull/ff"
license = "MIT/Apache-2.0"
repository = "https://github.com/ebfull/ff"
[lib]
proc-macro = true
[dependencies]
num-bigint = "0.2"
num-traits = "0.2"
num-integer = "0.1"
proc-macro2 = "0.4"
quote = "0.6"
syn = "0.14"

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#![allow(unused_imports)]
extern crate byteorder;
extern crate rand;
#[cfg(feature = "derive")]
#[macro_use]
extern crate ff_derive;
#[cfg(feature = "derive")]
pub use ff_derive::*;
use std::error::Error;
use std::fmt;
use std::io::{self, Read, Write};
/// This trait represents an element of a field.
pub trait Field:
Sized + Eq + Copy + Clone + Send + Sync + fmt::Debug + fmt::Display + 'static + rand::Rand
{
/// Returns the zero element of the field, the additive identity.
fn zero() -> Self;
/// Returns the one element of the field, the multiplicative identity.
fn one() -> Self;
/// Returns true iff this element is zero.
fn is_zero(&self) -> bool;
/// Squares this element.
fn square(&mut self);
/// Doubles this element.
fn double(&mut self);
/// Negates this element.
fn negate(&mut self);
/// Adds another element to this element.
fn add_assign(&mut self, other: &Self);
/// Subtracts another element from this element.
fn sub_assign(&mut self, other: &Self);
/// Multiplies another element by this element.
fn mul_assign(&mut self, other: &Self);
/// Computes the multiplicative inverse of this element, if nonzero.
fn inverse(&self) -> Option<Self>;
/// Exponentiates this element by a power of the base prime modulus via
/// the Frobenius automorphism.
fn frobenius_map(&mut self, power: usize);
/// Exponentiates this element by a number represented with `u64` limbs,
/// least significant digit first.
fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self {
let mut res = Self::one();
let mut found_one = false;
for i in BitIterator::new(exp) {
if found_one {
res.square();
} else {
found_one = i;
}
if i {
res.mul_assign(self);
}
}
res
}
}
/// This trait represents an element of a field that has a square root operation described for it.
pub trait SqrtField: Field {
/// Returns the Legendre symbol of the field element.
fn legendre(&self) -> LegendreSymbol;
/// Returns the square root of the field element, if it is
/// quadratic residue.
fn sqrt(&self) -> Option<Self>;
}
/// This trait represents a wrapper around a biginteger which can encode any element of a particular
/// prime field. It is a smart wrapper around a sequence of `u64` limbs, least-significant digit
/// first.
pub trait PrimeFieldRepr:
Sized
+ Copy
+ Clone
+ Eq
+ Ord
+ Send
+ Sync
+ Default
+ fmt::Debug
+ fmt::Display
+ 'static
+ rand::Rand
+ AsRef<[u64]>
+ AsMut<[u64]>
+ From<u64>
{
/// Subtract another represetation from this one.
fn sub_noborrow(&mut self, other: &Self);
/// Add another representation to this one.
fn add_nocarry(&mut self, other: &Self);
/// Compute the number of bits needed to encode this number. Always a
/// multiple of 64.
fn num_bits(&self) -> u32;
/// Returns true iff this number is zero.
fn is_zero(&self) -> bool;
/// Returns true iff this number is odd.
fn is_odd(&self) -> bool;
/// Returns true iff this number is even.
fn is_even(&self) -> bool;
/// Performs a rightwise bitshift of this number, effectively dividing
/// it by 2.
fn div2(&mut self);
/// Performs a rightwise bitshift of this number by some amount.
fn shr(&mut self, amt: u32);
/// Performs a leftwise bitshift of this number, effectively multiplying
/// it by 2. Overflow is ignored.
fn mul2(&mut self);
/// Performs a leftwise bitshift of this number by some amount.
fn shl(&mut self, amt: u32);
/// Writes this `PrimeFieldRepr` as a big endian integer.
fn write_be<W: Write>(&self, mut writer: W) -> io::Result<()> {
use byteorder::{BigEndian, WriteBytesExt};
for digit in self.as_ref().iter().rev() {
writer.write_u64::<BigEndian>(*digit)?;
}
Ok(())
}
/// Reads a big endian integer into this representation.
fn read_be<R: Read>(&mut self, mut reader: R) -> io::Result<()> {
use byteorder::{BigEndian, ReadBytesExt};
for digit in self.as_mut().iter_mut().rev() {
*digit = reader.read_u64::<BigEndian>()?;
}
Ok(())
}
/// Writes this `PrimeFieldRepr` as a little endian integer.
fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> {
use byteorder::{LittleEndian, WriteBytesExt};
for digit in self.as_ref().iter() {
writer.write_u64::<LittleEndian>(*digit)?;
}
Ok(())
}
/// Reads a little endian integer into this representation.
fn read_le<R: Read>(&mut self, mut reader: R) -> io::Result<()> {
use byteorder::{LittleEndian, ReadBytesExt};
for digit in self.as_mut().iter_mut() {
*digit = reader.read_u64::<LittleEndian>()?;
}
Ok(())
}
}
#[derive(Debug, PartialEq)]
pub enum LegendreSymbol {
Zero = 0,
QuadraticResidue = 1,
QuadraticNonResidue = -1,
}
/// An error that may occur when trying to interpret a `PrimeFieldRepr` as a
/// `PrimeField` element.
#[derive(Debug)]
pub enum PrimeFieldDecodingError {
/// The encoded value is not in the field
NotInField(String),
}
impl Error for PrimeFieldDecodingError {
fn description(&self) -> &str {
match *self {
PrimeFieldDecodingError::NotInField(..) => "not an element of the field",
}
}
}
impl fmt::Display for PrimeFieldDecodingError {
fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
match *self {
PrimeFieldDecodingError::NotInField(ref repr) => {
write!(f, "{} is not an element of the field", repr)
}
}
}
}
/// This represents an element of a prime field.
pub trait PrimeField: Field {
/// The prime field can be converted back and forth into this biginteger
/// representation.
type Repr: PrimeFieldRepr + From<Self>;
/// Interpret a string of numbers as a (congruent) prime field element.
/// Does not accept unnecessary leading zeroes or a blank string.
fn from_str(s: &str) -> Option<Self> {
if s.is_empty() {
return None;
}
if s == "0" {
return Some(Self::zero());
}
let mut res = Self::zero();
let ten = Self::from_repr(Self::Repr::from(10)).unwrap();
let mut first_digit = true;
for c in s.chars() {
match c.to_digit(10) {
Some(c) => {
if first_digit {
if c == 0 {
return None;
}
first_digit = false;
}
res.mul_assign(&ten);
res.add_assign(&Self::from_repr(Self::Repr::from(u64::from(c))).unwrap());
}
None => {
return None;
}
}
}
Some(res)
}
/// Convert this prime field element into a biginteger representation.
fn from_repr(Self::Repr) -> Result<Self, PrimeFieldDecodingError>;
/// Convert a biginteger representation into a prime field element, if
/// the number is an element of the field.
fn into_repr(&self) -> Self::Repr;
/// Returns the field characteristic; the modulus.
fn char() -> Self::Repr;
/// How many bits are needed to represent an element of this field.
const NUM_BITS: u32;
/// How many bits of information can be reliably stored in the field element.
const CAPACITY: u32;
/// Returns the multiplicative generator of `char()` - 1 order. This element
/// must also be quadratic nonresidue.
fn multiplicative_generator() -> Self;
/// 2^s * t = `char()` - 1 with t odd.
const S: u32;
/// Returns the 2^s root of unity computed by exponentiating the `multiplicative_generator()`
/// by t.
fn root_of_unity() -> Self;
}
/// An "engine" is a collection of types (fields, elliptic curve groups, etc.)
/// with well-defined relationships. Specific relationships (for example, a
/// pairing-friendly curve) can be defined in a subtrait.
pub trait ScalarEngine: Sized + 'static + Clone {
/// This is the scalar field of the engine's groups.
type Fr: PrimeField + SqrtField;
}
#[derive(Debug)]
pub struct BitIterator<E> {
t: E,
n: usize,
}
impl<E: AsRef<[u64]>> BitIterator<E> {
pub fn new(t: E) -> Self {
let n = t.as_ref().len() * 64;
BitIterator { t, n }
}
}
impl<E: AsRef<[u64]>> Iterator for BitIterator<E> {
type Item = bool;
fn next(&mut self) -> Option<bool> {
if self.n == 0 {
None
} else {
self.n -= 1;
let part = self.n / 64;
let bit = self.n - (64 * part);
Some(self.t.as_ref()[part] & (1 << bit) > 0)
}
}
}
#[test]
fn test_bit_iterator() {
let mut a = BitIterator::new([0xa953d79b83f6ab59, 0x6dea2059e200bd39]);
let expected = "01101101111010100010000001011001111000100000000010111101001110011010100101010011110101111001101110000011111101101010101101011001";
for e in expected.chars() {
assert!(a.next().unwrap() == (e == '1'));
}
assert!(a.next().is_none());
let expected = "1010010101111110101010000101101011101000011101110101001000011001100100100011011010001011011011010001011011101100110100111011010010110001000011110100110001100110011101101000101100011100100100100100001010011101010111110011101011000011101000111011011101011001";
let mut a = BitIterator::new([
0x429d5f3ac3a3b759,
0xb10f4c66768b1c92,
0x92368b6d16ecd3b4,
0xa57ea85ae8775219,
]);
for e in expected.chars() {
assert!(a.next().unwrap() == (e == '1'));
}
assert!(a.next().is_none());
}
pub use self::arith_impl::*;
mod arith_impl {
/// Calculate a - b - borrow, returning the result and modifying
/// the borrow value.
#[inline(always)]
pub fn sbb(a: u64, b: u64, borrow: &mut u64) -> u64 {
let tmp = (1u128 << 64) + u128::from(a) - u128::from(b) - u128::from(*borrow);
*borrow = if tmp >> 64 == 0 { 1 } else { 0 };
tmp as u64
}
/// Calculate a + b + carry, returning the sum and modifying the
/// carry value.
#[inline(always)]
pub fn adc(a: u64, b: u64, carry: &mut u64) -> u64 {
let tmp = u128::from(a) + u128::from(b) + u128::from(*carry);
*carry = (tmp >> 64) as u64;
tmp as u64
}
/// Calculate a + (b * c) + carry, returning the least significant digit
/// and setting carry to the most significant digit.
#[inline(always)]
pub fn mac_with_carry(a: u64, b: u64, c: u64, carry: &mut u64) -> u64 {
let tmp = (u128::from(a)) + u128::from(b) * u128::from(c) + u128::from(*carry);
*carry = (tmp >> 64) as u64;
tmp as u64
}
}